Information spectrum approach to the source channel separation theorem
Nir Elkayam, Meir Feder · 2014
A source-channel separation theorem for a general channel has recently been shown by Aggrawal et al.[1]. This theorem states that if there exists a coding scheme that achieves a maximum distortion level dmaxover a general channel W, then reliable communication can be accomplished over this channel at rates less than R(dmax), where R(·) is the rate distortion function of the source. The source, however, is essentially constrained to be discrete and memoryless (DMS). In this work we prove a stronger claim where the source is general, satisfying only a “sphere packing optimality” feature, and the channel is completely general. Furthermore, we show that if the channel satisfies the strong converse property as defined by Han & Verdú [2], then the same statement can be made with davg, the average distortion level, replacing dmax. Unlike the proofs in [1], we use information spectrum methods and the results can be quite easily extended to other situations.